Homogenization of a coupled incompressible Stokes-Cahn-Hilliard system modeling binary fluid mixture in a porous medium

A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are separated by an evolving diffuse interface of a finite width depending on the scale parameter epsilon in the considered model. At first, the existence of solution of a coupled system of partial differential equations at micro scale is investigated. We obtained the homogenized equations for the microscopic model via unfolding operator and two-scale convergence approach. (C) 2022 Elsevier Ltd. All rights reserved.